Solution Surfaces and Generalized Paths in Non-linear Structural Mechanics

The paper describes how quasi-static, conservative instability problems can be seen in a multi-dimensional context, and how one- and two-dimensional solution manifolds can reveal further information on the structural response. The discussed viewpoint can be seen as the natural extension of the common one-dimensional path-following methods, when additional variables are introduced to describe the parameter dependence in structural response, instability analyses and optimization. The paper describes the general setting of the generalized equilibrium problems, and discusses their numerical treatment for the cases of resulting one- and two-dimensional solution sets. Numerical examples show some applications of these models, and describe the possibilities and properties of the obtained solution sets.